Ancient Greek
Book 3
Pappus Alexandrinus, Synagoge 3.3
Not analysed yet
3 Ὅτι δὲ ἡ ΓΕ δύναται τὸ δὶς ὑπὸ ΓΖ ΗΘ, οὕτως ἔσταιε δῆλον ἐπεζεύχθω ἡ ΕΘ. ἐπεὶ τὸ ἀπὸ ΕΓ ἴσον ἐστὶν τοῖς ἀπὸ τῶν ΕΘ ΘΓ καὶ τῷ δὶς ὑπὸ ΓΘ ΘΗ, ἔστιν δὲ καὶ τὰ ἀπὸ ΕΘ ΘΖ ἴσα τῷ ἀπὸ ΕΖ καὶ τῷ δὶς ὑπὸ ΖΘ ΘΗ ,ἴσα ἄρα καὶ τὰ ἀπὸ ΓΕ ΕΘ ΘΖ τοῖς ἀπὸ ΕΘ ΘΓ ΕΖ καὶ τῷ δὶς ὑπὸ ΓΘΗ μετὰ τοῦ δὶς ὑπὸ ΖΘΗ, τουτέστιν τῷ δὶς ὑπὸ ΓΖ ΗΘ. κοινὸν ἀφῃρήσθω τὸ ἀπὸ ΕΘ· λοιπὰ ἄρα τὰ ἀπὸ ΕΓ ΖΘ ἴσα ἐστὶν τοῖς ἀπὸ ΕΖ ΘΓ καὶ τῷ δὶς ὑπὸ ΓΖ ΗΘ. ὧν τὸ ἀπὸ ΖΘ ἴσον τοῖς ἀπὸ τῶν ΕΖ ΘΓ (τὸ μὲν γὰρ ἀπὸ τῆς ΖΘ ἐστὶν κε΄, τὸ δὲ ἀπὸ τῆς ΘΓ θʼ, καὶ τὸ ἀπὸ ΕΖ ιϚ΄)· λοιπὸν ἄρα τὸ ἀπὸ ΓΕ ἴσον ἐστὶν τῷ δὶς ὑπὸ ΖΓ ΗΘ.